Question

Evaluate: ${cosec}^2(90-\theta )-{tan}^2\theta$

Answer 1

$cose{c}^2(90-\theta )-{\tan }^2\theta$

$=\left[cosec\right(90-\theta ){]}^2-{\tan }^2\theta$

$={\sec }^2\theta -{\tan }^2\theta$ $[\because cosec(90-\theta )=\sec \theta ]$

$=1$.